Determinant representation for some transition probabilities in the TASEP with second class particles

We study the transition probabilities for the totally asymmetric simple exclusion process (TASEP) on the infinite integer lattice with a finite, but arbitrary number of first and second class particles. Using the Bethe ansatz we present an explicit expression of these quantities in terms of the Bethe wave function. In a next step it is proved rigorously that this expression can be written in a compact determinantal form for the case where the order of the first and second class particles does not change in time. An independent geometrical approach provides insight into these results and enables us to generalize the determinantal solution to the multi-class TASEP.Comment: Minor revision; journal reference adde

Crossover from 2-dimensional to 1-dimensional collective pinning in NbSe3

We have fabricated NbSe$_3$ structures with widths comparable to the Fukuyama-Lee-Rice phase-coherence length. For samples already in the 2-dimensional pinning limit, we observe a crossover from 2-dimensional to 1-dimensional collective pinning when the crystal width is less than 1.6 $\mu$m, corresponding to the phase-coherence length in this direction. Our results show that surface pinning is negligible in our samples, and provide a means to probe the dynamics of single domains giving access to a new regime in charge-density wave physics.Comment: 4 pages, 2 figures, and 1 table. Accepted for publication in Physical Review

Asymptotics of orthogonal polynomials for a weight with a jump on [−1,1]

We consider the orthogonal polynomials on [-1, 1] with respect to the weight w(c)(x) = h(x)(1 - x)(alpha) (1+ x)beta Xi(c)(x), alpha, beta > -1, where h is real analytic and strictly positive on [-1, 1] and Xi(c) is a step-like function: Xi(c)(x) = 1 for x is an element of [-1, 0) and Xi(c) (x) = c(2), c > 0, for x is an element of [0, 1]. We obtain strong uniform asymptotics of the monic orthogonal polynomials in C, as well as first terms of the asymptotic expansion of the main parameters (leading coefficients of the orthonormal polynomials and the recurrence coefficients) as n -> infinity. In particular, we prove for w(c) a conjecture of A. Magnus regarding the asymptotics of the recurrence coefficients. The main focus is on the local analysis at the origin. We study the asymptotics of the Christoffel-Darboux kernel in a neighborhood of the jump and show that the zeros of the orthogonal polynomials no longer exhibit clock behavior. For the asymptotic analysis we use the steepest descent method of Deift and Zhou applied to the noncommutative Riemann-Hilbert problems characterizing the orthogonal polynomials. The local analysis at x = 0 is carried out in terms of confluent hypergeometric functions. Incidentally, we establish some properties of these functions that may have an independent interest.Junta de Andalucía-Spain- FQM-229 and P06- FQM-01735.Ministry of Science and Innovation of Spain - MTM2008-06689-C02-01FCT -SFRH/BD/29731/200

On the mechanisms governing gas penetration into a tokamak plasma during a massive gas injection

A new 1D radial fluid code, IMAGINE, is used to simulate the penetration of gas into a tokamak plasma during a massive gas injection (MGI). The main result is that the gas is in general strongly braked as it reaches the plasma, due to mechanisms related to charge exchange and (to a smaller extent) recombination. As a result, only a fraction of the gas penetrates into the plasma. Also, a shock wave is created in the gas which propagates away from the plasma, braking and compressing the incoming gas. Simulation results are quantitatively consistent, at least in terms of orders of magnitude, with experimental data for a D 2 MGI into a JET Ohmic plasma. Simulations of MGI into the background plasma surrounding a runaway electron beam show that if the background electron density is too high, the gas may not penetrate, suggesting a possible explanation for the recent results of Reux et al in JET (2015 Nucl. Fusion 55 093013)

Fast Distributed Coloring Algorithms for Triangle-Free Graphs

Vertex coloring is a central concept in graph theory and an important symmetry-breaking primitive in distributed computing. Whereas degree- ∆ graphs may require palettes of ∆+1 colors in the worst case, it is well known that the chromatic number of many natural graph classes can be much smaller. In this paper we give new distributed algorithms to find (∆/k)-coloring in graphs of girth 4 (triangle-free graphs), girth 5, and trees, where k is at most ( 1 4 − o(1)) ln ∆ in triangle-free graphs and at most (1 − o(1)) ln ∆ in girth-5 graphs and trees, and o(1) is a function of ∆. Specifically,for∆sufficiently large we can find such a coloring in O(k +log ∗ n)time.Moreover,forany ∆ we can compute such colorings in roughly logarithmic time for triangle-free and girth-5 graphs, and in O(log ∆ +log∆log n) time on trees. As a byproduct, our algorithm shows that the chromatic number of triangle-free graphs is at most (4 + o(1)) ∆ ln ∆, which improves on Jamall’s recent bound of (67 + o(1)) ∆ ln ∆ 1. Also, we show that (∆+1)-coloring for triangle-free graphs can be obtained in sublogarithmic time for any ∆